When a quark emits or absorbs a gluon, that
quark's color must change in order to conserve color charge.
For example, suppose a red quark
changes into a blue quark and emits a red/antiblue gluon (the image below illustrates antiblue as yellow).
The net color is still red. This is because - after the emission of the gluon - the blue
color of the quark cancels with the antiblue color of the gluon. The remaining color then is the
red color of the gluon.

Quarks emit and absorb gluons very frequently within a hadron,
so there is no way to observe the color of an individual quark.
Within a hadron, though, the color of the two quarks exchanging a gluon
will change in a way that keeps the bound system in a color-neutral
state.